New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-3835

Keywords:

Hermite-Hadamard inequality, Convex functions on the coordinates, m-convex functions on the coordinates, (α, m)-convex functions on the coordinates, Hölder’s inequality, Katugampola fractional integrals

Abstract

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

Author Biography

Seth Kermausuor, Alabama State University.

Department of Mathematics and Computer Science.

References

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Published

2021-11-29

How to Cite

[1]
S. Kermausuor, “New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals”, Proyecciones (Antofagasta, On line), vol. 40, no. 6, pp. 1449-1472, Nov. 2021.

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Artículos